Instability in pipe flow

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 105; no. 2; pp. 428 - 430
• Main Authors: Cotrell, D.L, McFadden, G.B, Alder, B.J
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 15-01-2008; National Acad Sciences
• Subjects: Amplitude; Base flow; Boundary conditions; Flow velocity; Fluid dynamics; Mathematical extrapolation; Physical Sciences; Physics; Pipe flow; Pipes; Radial velocity; Reynolds number; Wave velocity; Wavelengths
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0709172104

The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.